OpenRaiser/Intern-Atlas huggingface dataset:
The two-edge connectivity survivable-network design problem in planar graphs
Venue: arXiv cs.DS 2015
Year: 2015

Consider the following problem: given a graph with edge costs and a subset Q of vertices, find a minimum-cost subgraph in which there are two edge-disjoint paths connecting every pair of vertices in Q. The problem is a failure-resilient analog of the Steiner tree problem arising, for example, in telecommunications applications. We study a more general mixed-connectivity formulation, also employed in telecommunications optimization. Given a number (or requirement) r(v) in {0, 1, 2} for each vertex v in the graph, find a minimum-cost subgraph in which there are min{r(u), r(v)} edge-disjoint u-to-v paths for every pair u, v of vertices. We address the problem in planar graphs, considering a popular relaxation in which the solution is allowed to use multiple copies of the input-graph edges (paying separately for each copy). The problem is max SNP-hard in general graphs and strongly NP-hard in planar graphs. We give the first polynomial-time approximation scheme in planar graphs. The running time is O(n log n). Under the additional restriction that the requirements are only non-zero for vertices on the boundary of a single face of a planar graph, we give a polynomial-time algorithm to find the optimal solution.
Diffuse Reflection Diameter in Simple Polygons
Venue: arXiv cs.CG 2015
Year: 2015

We prove a conjecture of Aanjaneya, Bishnu, and Pal that the minimum number of diffuse reflections sufficient to illuminate the interior of any simple polygon with $n$ walls from any interior point light source is $\lfloor n/2 \rfloor - 1$. Light reflecting diffusely leaves a surface in all directions, rather than at an identical angle as with specular reflections.
An Improved Integrality Gap for Asymmetric TSP Paths
Venue: arXiv cs.DS 2015
Year: 2015

The Asymmetric Traveling Salesperson Path Problem (ATSPP) is one where, given an asymmetric metric space $(V,d)$ with specified vertices s and t, the goal is to find an s-t path of minimum length that passes through all the vertices in V. This problem is closely related to the Asymmetric TSP (ATSP), which seeks to find a tour (instead of an $s-t$ path) visiting all the nodes: for ATSP, a $ρ$-approximation guarantee implies an $O(ρ)$-approximation for ATSPP. However, no such connection is known for the integrality gaps of the linear programming relaxations for these problems: the current-best approximation algorithm for ATSPP is $O(\log n/\log\log n)$, whereas the best bound on the integrality gap of the natural LP relaxation (the subtour elimination LP) for ATSPP is $O(\log n)$. In this paper, we close this gap, and improve the current best bound on the integrality gap from $O(\log n)$ to $O(\log n/\log\log n)$. The resulting algorithm uses the structure of narrow $s$-$t$ cuts in the LP solution to construct a (random) tree spanning tree that can be cheaply augmented to contain an Eulerian $s$-$t$ walk. We also build on a result of Oveis Gharan and Saberi and show a strong form of Goddyn's conjecture about thin spanning trees implies the integrality gap of the subtour elimination LP relaxation for ATSPP is bounded by a constant. Finally, we give a simpler family of instances showing the integrality gap of this LP is at least 2.
Decision-Theoretic Troubleshooting: A Framework for Repair and Experiment
Venue: arXiv cs.AI 2015
Year: 2015

We develop and extend existing decision-theoretic methods for troubleshooting a nonfunctioning device. Traditionally, diagnosis with Bayesian networks has focused on belief updating---determining the probabilities of various faults given current observations. In this paper, we extend this paradigm to include taking actions. In particular, we consider three classes of actions: (1) we can make observations regarding the behavior of a device and infer likely faults as in traditional diagnosis, (2) we can repair a component and then observe the behavior of the device to infer likely faults, and (3) we can change the configuration of the device, observe its new behavior, and infer the likelihood of faults. Analysis of latter two classes of troubleshooting actions requires incorporating notions of persistence into the belief-network formalism used for probabilistic inference.
Asymptotic Model Selection for Directed Networks with Hidden Variables
Venue: arXiv cs.LG 2015
Year: 2015

We extend the Bayesian Information Criterion (BIC), an asymptotic approximation for the marginal likelihood, to Bayesian networks with hidden variables. This approximation can be used to select models given large samples of data. The standard BIC as well as our extension punishes the complexity of a model according to the dimension of its parameters. We argue that the dimension of a Bayesian network with hidden variables is the rank of the Jacobian matrix of the transformation between the parameters of the network and the parameters of the observable variables. We compute the dimensions of several networks including the naive Bayes model with a hidden root node.
Digital morphogenesis via Schelling segregation
Venue: arXiv cs.GT 2015
Year: 2015

Schelling's model of segregation looks to explain the way in which particles or agents of two types may come to arrange themselves spatially into configurations consisting of large homogeneous clusters, i.e.\ connected regions consisting of only one type. As one of the earliest agent based models studied by economists and perhaps the most famous model of self-organising behaviour, it also has direct links to areas at the interface between computer science and statistical mechanics, such as the Ising model and the study of contagion and cascading phenomena in networks. While the model has been extensively studied it has largely resisted rigorous analysis, prior results from the literature generally pertaining to variants of the model which are tweaked so as to be amenable to standard techniques from statistical mechanics or stochastic evolutionary game theory. In \cite{BK}, Brandt, Immorlica, Kamath and Kleinberg provided the first rigorous analysis of the unperturbed model, for a specific set of input parameters. Here we provide a rigorous analysis of the model's behaviour much more generally and establish some surprising forms of threshold behaviour, notably the existence of situations where an \emph{increased} level of intolerance for neighbouring agents of opposite type leads almost certainly to \emph{decreased} segregation.
A New Look at Causal Independence
Venue: arXiv cs.AI 2015
Year: 2015

Heckerman (1993) defined causal independence in terms of a set of temporal conditional independence statements. These statements formalized certain types of causal interaction where (1) the effect is independent of the order that causes are introduced and (2) the impact of a single cause on the effect does not depend on what other causes have previously been applied. In this paper, we introduce an equivalent a temporal characterization of causal independence based on a functional representation of the relationship between causes and the effect. In this representation, the interaction between causes and effect can be written as a nested decomposition of functions. Causal independence can be exploited by representing this decomposition in the belief network, resulting in representations that are more efficient for inference than general causal models. We present empirical results showing the benefits of a causal-independence representation for belief-network inference.
Injectivity w.r.t. Distribution of Elements in the Compressed Sequences Derived from Primitive Sequences over $Z/p^eZ$
Venue: arXiv cs.IT 2015
Year: 2015

Let $p\geq3$ be a prime and $e\geq2$ an integer. Let $σ(x)$ be a primitive polynomial of degree $n$ over $Z/p^eZ$ and $G'(σ(x),p^e)$ the set of primitive linear recurring sequences generated by $σ(x)$. A compressing map $φ$ on $Z/p^eZ$ naturally induces a map $\hatφ$ on $G'(σ(x),p^e)$. For a subset $D$ of the image of $φ$,$\hatφ$ is called to be injective w.r.t. $D$-uniformity if the distribution of elements of $D$ in the compressed sequence implies all information of the original primitive sequence. In this correspondence, for at least $1-2(p-1)/(p^n-1)$ of primitive polynomials of degree $n$, a clear criterion on $φ$ is obtained to decide whether $\hatφ$ is injective w.r.t. $D$-uniformity, and the majority of maps on $Z/p^eZ$ induce injective maps on $G'(σ(x),p^e)$. Furthermore, a sufficient condition on $φ$ is given to ensure injectivity of $\hatφ$ w.r.t. $D$-uniformity. It follows from the sufficient condition that if $σ(x)$ is strongly primitive and the compressing map $φ(x)=f(x_{e-1})$, where $f(x_{e-1})$ is a permutation polynomial over $\mathbb{F}_{p}$, then $\hatφ$ is injective w.r.t. $D$-uniformity for $\emptyset\neq D\subset\mathbb{F}_{p}$. Moreover, we give three specific families of compressing maps which induce injective maps on $G'(σ(x),p^e)$.
Inference Algorithms for Similarity Networks
Venue: arXiv cs.AI 2015
Year: 2015

We examine two types of similarity networks each based on a distinct notion of relevance. For both types of similarity networks we present an efficient inference algorithm that works under the assumption that every event has a nonzero probability of occurrence. Another inference algorithm is developed for type 1 similarity networks that works under no restriction, albeit less efficiently.
Oracle Pushdown Automata, Nondeterministic Reducibilities, and the CFL Hierarchy over the Family of Context-Free Languages
Venue: arXiv cs.FL 2015
Year: 2015

To expand a fundamental theory of context-free languages, we equip nondeterministic one-way pushdown automata with additional oracle mechanisms, which naturally induce various nondeterministic reducibilities among formal languages. As a natural restriction of NP-reducibility, we introduce a notion of many-one CFL reducibility and conduct a ground work to formulate a coherent framework for further expositions. Two more powerful reducibilities--bounded truth-table and Turing CFL-reducibilities--are also discussed in comparison. The Turing CFL-reducibility, in particular, helps us introduce an exquisite hierarchy, called the CFL hierarchy, built over the family CFL of context-free languages. For each level of this hierarchy, its basic structural properties are proven and three alternative characterizations are presented. The second level is not included in NC(2) unless NP= NC(2). The first and second levels of the hierarchy are different. The rest of the hierarchy (more strongly, the Boolean hierarchy built over each level of the hierarchy) is also infinite unless the polynomial hierarchy over NP collapses. This follows from a characterization of the Boolean hierarchy over the k-th level of the polynomial hierarchy in terms of the Boolean hierarchy over the k+1st level of the CFL hierarchy using log-space many-one reductions. Similarly, the complexity class Theta(k) is related to the closure of the k-th level of the CFL hierarchy under log-space truth-table reductions. We also argue that the CFL hierarchy coincides with a hierarchy over CFL built by application of many-one CFL-reductions. We show that BPCFL--a bounded-error probabilistic version of CFL--is not included in CFL even in the presence of advice. Employing a known circuit lower bound and a switching lemma, we exhibit a relativized world where BPCFL is not located within the second level of the CFL hierarchy.
Toggling a Genetic Switch Using Reinforcement Learning
Venue: arXiv cs.SY 2015
Year: 2015

In this paper, we consider the problem of optimal exogenous control of gene regulatory networks. Our approach consists in adapting an established reinforcement learning algorithm called the fitted Q iteration. This algorithm infers the control law directly from the measurements of the system's response to external control inputs without the use of a mathematical model of the system. The measurement data set can either be collected from wet-lab experiments or artificially created by computer simulations of dynamical models of the system. The algorithm is applicable to a wide range of biological systems due to its ability to deal with nonlinear and stochastic system dynamics. To illustrate the application of the algorithm to a gene regulatory network, the regulation of the toggle switch system is considered. The control objective of this problem is to drive the concentrations of two specific proteins to a target region in the state space.
Optimal Control of Two-Player Systems with Output Feedback
Venue: arXiv cs.SY 2015
Year: 2015

In this article, we consider a fundamental decentralized optimal control problem, which we call the two-player problem. Two subsystems are interconnected in a nested information pattern, and output feedback controllers must be designed for each subsystem. Several special cases of this architecture have previously been solved, such as the state-feedback case or the case where the dynamics of both systems are decoupled. In this paper, we present a detailed solution to the general case. The structure of the optimal decentralized controller is reminiscent of that of the optimal centralized controller; each player must estimate the state of the system given their available information and apply static control policies to these estimates to compute the optimal controller. The previously solved cases benefit from a separation between estimation and control which allows one to compute the control and estimation gains separately. This feature is not present in general, and some of the gains must be solved for simultaneously. We show that computing the required coupled estimation and control gains amounts to solving a small system of linear equations.
A Quorum Sensing Inspired Algorithm for Dynamic Clustering
Venue: arXiv cs.LG 2015
Year: 2015

Quorum sensing is a decentralized biological process, through which a community of cells with no global awareness coordinate their functional behaviors based solely on cell-medium interactions and local decisions. This paper draws inspirations from quorum sensing and colony competition to derive a new algorithm for data clustering. The algorithm treats each data as a single cell, and uses knowledge of local connectivity to cluster cells into multiple colonies simultaneously. It simulates auto-inducers secretion in quorum sensing to tune the influence radius for each cell. At the same time, sparsely distributed core cells spread their influences to form colonies, and interactions between colonies eventually determine each cell's identity. The algorithm has the flexibility to analyze not only static but also time-varying data, which surpasses the capacity of many existing algorithms. Its stability and convergence properties are established. The algorithm is tested on several applications, including both synthetic and real benchmarks data sets, alleles clustering, community detection, image segmentation. In particular, the algorithm's distinctive capability to deal with time-varying data allows us to experiment it on novel applications such as robotic swarms grouping and switching model identification. We believe that the algorithm's promising performance would stimulate many more exciting applications.
Advances in Probabilistic Reasoning
Venue: arXiv cs.AI 2015
Year: 2015

This paper discuses multiple Bayesian networks representation paradigms for encoding asymmetric independence assertions. We offer three contributions: (1) an inference mechanism that makes explicit use of asymmetric independence to speed up computations, (2) a simplified definition of similarity networks and extensions of their theory, and (3) a generalized representation scheme that encodes more types of asymmetric independence assertions than do similarity networks.
Macro Lambda Calculus
Venue: arXiv cs.LO 2015
Year: 2015

The goal of our Macro Lambda Calculus project (MLC) is to encode lambda terms into interaction nets. Its software implementation will accept input in the notation similar to lambda calculus allowing macro definitions. Output is similar to interaction calculus and is suitable for our Interaction Nets Compiler program (INC). In this paper, we describe the interaction system for call-by-need evaluation and the mechanism of encoding lambda terms into this system which MLC is based on.
The local-global conjecture for scheduling with non-linear cost
Venue: arXiv cs.DS 2015
Year: 2015

We consider the classical scheduling problem on a single machine, on which we need to schedule sequentially $n$ given jobs. Every job $j$ has a processing time $p_j$ and a priority weight $w_j$, and for a given schedule a completion time $C_j$. In this paper we consider the problem of minimizing the objective value $\sum_j w_j C_j^β$ for some fixed constant $β>0$. This non-linearity is motivated for example by the learning effect of a machine improving its efficiency over time, or by the speed scaling model. For $β=1$, the well-known Smith's rule that orders job in the non-increasing order of $w_j/p_j$ give the optimum schedule. However, for $β\neq 1$, the complexity status of this problem is open. Among other things, a key issue here is that the ordering between a pair of jobs is not well-defined, and might depend on where the jobs lie in the schedule and also on the jobs between them. We investigate this question systematically and substantially generalize the previously known results in this direction. These results lead to interesting new dominance properties among schedules which lead to huge speed up in exact algorithms for the problem. An experimental study evaluates the impact of these properties on the exact algorithm A*.
Chip-level and multi-node analysis of energy-optimized lattice-Boltzmann CFD simulations
Venue: arXiv cs.PF 2015
Year: 2015

Memory-bound algorithms show complex performance and energy consumption behavior on multicore processors. We choose the lattice-Boltzmann method (LBM) on an Intel Sandy Bridge cluster as a prototype scenario to investigate if and how single-chip performance and power characteristics can be generalized to the highly parallel case. First we perform an analysis of a sparse-lattice LBM implementation for complex geometries. Using a single-core performance model, we predict the intra-chip saturation characteristics and the optimal operating point in terms of energy to solution as a function of implementation details, clock frequency, vectorization, and number of active cores per chip. We show that high single-core performance and a correct choice of the number of active cores per chip are the essential optimizations for lowest energy to solution at minimal performance degradation. Then we extrapolate to the MPI-parallel level and quantify the energy-saving potential of various optimizations and execution modes, where we find these guidelines to be even more important, especially when communication overhead is non-negligible. In our setup we could achieve energy savings of 35% in this case, compared to a naive approach. We also demonstrate that a simple non-reflective reduction of the clock speed leaves most of the energy saving potential unused.
Computing a k-sparse n-length Discrete Fourier Transform using at most 4k samples and O(k log k) complexity
Venue: arXiv cs.DS 2015
Year: 2015

Given an $n$-length input signal $\mbf{x}$, it is well known that its Discrete Fourier Transform (DFT), $\mbf{X}$, can be computed in $O(n \log n)$ complexity using a Fast Fourier Transform (FFT). If the spectrum $\mbf{X}$ is exactly $k$-sparse (where $k<<n$), can we do better? We show that asymptotically in $k$ and $n$, when $k$ is sub-linear in $n$ (precisely, $k \propto n^δ$ where $0 < δ<1$), and the support of the non-zero DFT coefficients is uniformly random, we can exploit this sparsity in two fundamental ways (i) {\bf {sample complexity}}: we need only $M=rk$ deterministically chosen samples of the input signal $\mbf{x}$ (where $r < 4$ when $0 < δ< 0.99$); and (ii) {\bf {computational complexity}}: we can reliably compute the DFT $\mbf{X}$ using $O(k \log k)$ operations, where the constants in the big Oh are small and are related to the constants involved in computing a small number of DFTs of length approximately equal to the sparsity parameter $k$. Our algorithm succeeds with high probability, with the probability of failure vanishing to zero asymptotically in the number of samples acquired, $M$.
High-level Counterexamples for Probabilistic Automata
Venue: arXiv cs.SE 2015
Year: 2015

Providing compact and understandable counterexamples for violated system properties is an essential task in model checking. Existing works on counterexamples for probabilistic systems so far computed either a large set of system runs or a subset of the system's states, both of which are of limited use in manual debugging. Many probabilistic systems are described in a guarded command language like the one used by the popular model checker PRISM. In this paper we describe how a smallest possible subset of the commands can be identified which together make the system erroneous. We additionally show how the selected commands can be further simplified to obtain a well-understandable counterexample.
Auditing: Active Learning with Outcome-Dependent Query Costs
Venue: arXiv cs.LG 2015
Year: 2015

We propose a learning setting in which unlabeled data is free, and the cost of a label depends on its value, which is not known in advance. We study binary classification in an extreme case, where the algorithm only pays for negative labels. Our motivation are applications such as fraud detection, in which investigating an honest transaction should be avoided if possible. We term the setting auditing, and consider the auditing complexity of an algorithm: the number of negative labels the algorithm requires in order to learn a hypothesis with low relative error. We design auditing algorithms for simple hypothesis classes (thresholds and rectangles), and show that with these algorithms, the auditing complexity can be significantly lower than the active label complexity. We also discuss a general competitive approach for auditing and possible modifications to the framework.
Fast Marching Tree: a Fast Marching Sampling-Based Method for Optimal Motion Planning in Many Dimensions
Venue: arXiv cs.RO 2015
Year: 2015

In this paper we present a novel probabilistic sampling-based motion planning algorithm called the Fast Marching Tree algorithm (FMT*). The algorithm is specifically aimed at solving complex motion planning problems in high-dimensional configuration spaces. This algorithm is proven to be asymptotically optimal and is shown to converge to an optimal solution faster than its state-of-the-art counterparts, chiefly PRM* and RRT*. The FMT* algorithm performs a "lazy" dynamic programming recursion on a predetermined number of probabilistically-drawn samples to grow a tree of paths, which moves steadily outward in cost-to-arrive space. As a departure from previous analysis approaches that are based on the notion of almost sure convergence, the FMT* algorithm is analyzed under the notion of convergence in probability: the extra mathematical flexibility of this approach allows for convergence rate bounds--the first in the field of optimal sampling-based motion planning. Specifically, for a certain selection of tuning parameters and configuration spaces, we obtain a convergence rate bound of order $O(n^{-1/d+ρ})$, where $n$ is the number of sampled points, $d$ is the dimension of the configuration space, and $ρ$ is an arbitrarily small constant. We go on to demonstrate asymptotic optimality for a number of variations on FMT*, namely when the configuration space is sampled non-uniformly, when the cost is not arc length, and when connections are made based on the number of nearest neighbors instead of a fixed connection radius. Numerical experiments over a range of dimensions and obstacle configurations confirm our theoretical and heuristic arguments by showing that FMT*, for a given execution time, returns substantially better solutions than either PRM* or RRT*, especially in high-dimensional configuration spaces and in scenarios where collision-checking is expensive.